Problem: Factor completely. $4p^2-25q^2=$
Explanation: $4 p ^2 -25 q ^2 = ({2 p })^2-({5 q })^2$ Using the difference of squares pattern: $({2 p })^2 - ({5 q })^2 =({2 p }+{5 q })({2 p }-{5 q })$ In conclusion, $4 p ^2-25 q ^2=(2 p +5 q )(2 p -5 q )$ Remember that you can always check your factorization by expanding it.